How has Stochastic calculus changed the way we think and/or design systems?
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I am an outsider to the field of Stochastic calculus, and I was reading about the historical developments in the field: from Louis Bachelier, Einstein, to Ito, and other pioneers in the field. I see how the approach can be used to explain/model phenomena that can otherwise prove difficult to model.
I have also been trying to see if this field has helped in ways other than modeling/explaining phenomena:
- Are there fundamental insights from this field that have predicted phenomena that were non-intuitive/non-obvious, that necessarily needed Stochastic calculus as a tool?
- Did the insights help us design "better" systems? For example: Ordinary differential equations are often used to model control systems, which can be used to design stable systems that have desirable properties, such as quick convergence, etc. Are there similar results, or even impossibility results, from Stochastic calculus?
stochastic-calculus stochastic-analysis
asked Dec 12 '18 at 19:46
VimalVimal
1234
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add a comment |
$begingroup$
I am an outsider to the field of Stochastic calculus, and I was reading about the historical developments in the field: from Louis Bachelier, Einstein, to Ito, and other pioneers in the field. I see how the approach can be used to explain/model phenomena that can otherwise prove difficult to model.
I have also been trying to see if this field has helped in ways other than modeling/explaining phenomena:
- Are there fundamental insights from this field that have predicted phenomena that were non-intuitive/non-obvious, that necessarily needed Stochastic calculus as a tool?
- Did the insights help us design "better" systems? For example: Ordinary differential equations are often used to model control systems, which can be used to design stable systems that have desirable properties, such as quick convergence, etc. Are there similar results, or even impossibility results, from Stochastic calculus?
stochastic-calculus stochastic-analysis
asked Dec 12 '18 at 19:46
VimalVimal
1234
$endgroup$
1
$begingroup$
Derivatives Pricing theory is a very huge result of stochastic. Modern finance would not exist without it
$endgroup$
– NazimJ
Dec 12 '18 at 20:00
add a comment |
$begingroup$
I am an outsider to the field of Stochastic calculus, and I was reading about the historical developments in the field: from Louis Bachelier, Einstein, to Ito, and other pioneers in the field. I see how the approach can be used to explain/model phenomena that can otherwise prove difficult to model.
I have also been trying to see if this field has helped in ways other than modeling/explaining phenomena:
- Are there fundamental insights from this field that have predicted phenomena that were non-intuitive/non-obvious, that necessarily needed Stochastic calculus as a tool?
- Did the insights help us design "better" systems? For example: Ordinary differential equations are often used to model control systems, which can be used to design stable systems that have desirable properties, such as quick convergence, etc. Are there similar results, or even impossibility results, from Stochastic calculus?
stochastic-calculus stochastic-analysis
asked Dec 12 '18 at 19:46
VimalVimal
1234
$endgroup$
I am an outsider to the field of Stochastic calculus, and I was reading about the historical developments in the field: from Louis Bachelier, Einstein, to Ito, and other pioneers in the field. I see how the approach can be used to explain/model phenomena that can otherwise prove difficult to model.
I have also been trying to see if this field has helped in ways other than modeling/explaining phenomena:
- Are there fundamental insights from this field that have predicted phenomena that were non-intuitive/non-obvious, that necessarily needed Stochastic calculus as a tool?
- Did the insights help us design "better" systems? For example: Ordinary differential equations are often used to model control systems, which can be used to design stable systems that have desirable properties, such as quick convergence, etc. Are there similar results, or even impossibility results, from Stochastic calculus?
stochastic-calculus stochastic-analysis
stochastic-calculus stochastic-analysis
asked Dec 12 '18 at 19:46
VimalVimal
1234
asked Dec 12 '18 at 19:46
VimalVimal
1234
asked Dec 12 '18 at 19:46
VimalVimal
1234
asked Dec 12 '18 at 19:46
VimalVimal
1234
asked Dec 12 '18 at 19:46
VimalVimal
1234
1234
1
$begingroup$
Derivatives Pricing theory is a very huge result of stochastic. Modern finance would not exist without it
$endgroup$
– NazimJ
Dec 12 '18 at 20:00
add a comment |
1
$begingroup$
Derivatives Pricing theory is a very huge result of stochastic. Modern finance would not exist without it
$endgroup$
– NazimJ
Dec 12 '18 at 20:00
1
1
$begingroup$
Derivatives Pricing theory is a very huge result of stochastic. Modern finance would not exist without it
$endgroup$
– NazimJ
Dec 12 '18 at 20:00
$begingroup$
Derivatives Pricing theory is a very huge result of stochastic. Modern finance would not exist without it
$endgroup$
– NazimJ
Dec 12 '18 at 20:00
add a comment |
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Derivatives Pricing theory is a very huge result of stochastic. Modern finance would not exist without it
$endgroup$
– NazimJ
Dec 12 '18 at 20:00